• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.4 s.97
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• pp.474-482
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• 2005

A theoretical method is presented to investigate the thermoelastic and dynamic response of functionally graded material (FGM) rectangular plates made up of metal and ceramic. The temperature is assumed to be constant in the plane of the plate and to vary in the thickness direction only. Material properties are assumed to be temperature-dependant, and vary continuously through the thickness according to a power law distribution in terms of the volume fraction of the constituents. The third order shear deformation theory (TSDT) to account for rotary inertia and transverse shear strains is adopted to formulate the theoretical model. The modal analysis technique is used to develop the analytic solutions of the dynamic problem. The effect of material compositions and temperature fields is examined. The present theoretical results are verified by comparing with those from finite element analysis by ANSYS.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.11
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• pp.1119-1125
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• 2009

The coupled fluid-structure interaction problem is analyzed using the theoretical method to investigate the coupled vibration characteristics of functionally graded material(FGM) cylindrical shells conveying an incompressible, inviscid fluid. Material properties are assumed to vary continuously through the thickness according to a power law distribution in terms of the volume fraction of the constituents. The steady flow of fluid is described by the classical potential flow theory. The motion of shell represented by the first order shear deformation theory(FSDT) to account for rotary inertia and transverse shear strains. The effect of internal fluid can be taken into consideration by imposing a relation between the fluid pressure and the radial displacement of the structure at the interface. Numerical examples are presented and compared with exiting results.

• Smart Structures and Systems
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• v.19 no.4
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• pp.441-448
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• 2017

This paper uses the four-variable refined plate theory for the free vibration analysis of functionally graded material (FGM) rectangular plates. The plate properties are assumed to be varied through the thickness following a simple power law distribution in terms of volume fraction of material constituents. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. Equations of motion are derived from the Hamilton's principle. The closed-form solutions of functionally graded plates are obtained using Navier solution. Numerical results of the refined plate theory are presented to show the effect of the material distribution, the aspect and side-to-thickness ratio on the fundamental frequencies. It can be concluded that the proposed theory is accurate and simple in solving the free vibration behavior of functionally graded plates.

• Structural Engineering and Mechanics
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• v.60 no.2
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• pp.313-335
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• 2016

In this article, a four-variable refined plate theory is presented for buckling analysis of functionally graded plates subjected to uniform, linear and non-linear temperature rises across the thickness direction. The theory accounts for parabolic distribution of the transverse shear strains, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. Young's modulus and Poisson ratio of the FGM plates are assumed to remain constant throughout the entire plate. However, the coefficient of thermal expansion of the FGM plate varies according to a power law form through the thickness coordinate. Equilibrium and stability equations are derived based on the present theory. The influences of many plate parameters on buckling temperature difference such ratio of thermal expansion, aspect ratio, side-to-thickness ratio and gradient index will be investigated.

• Structural Engineering and Mechanics
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• v.49 no.6
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• pp.727-743
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• 2014

Geometrically nonlinear analysis of planar beam and frame structures made of functionally graded material (FGM) by using the finite element method is presented. The material property of the structures is assumed to be graded in the thickness direction by a power law distribution. A nonlinear beam element based on Bernoulli beam theory, taking the shift of the neutral axis position into account, is formulated in the context of the co-rotational formulation. The nonlinear equilibrium equations are solved by using the incremental/iterative procedure in a combination with the arc-length control method. Numerical examples show that the formulated element is capable to give accurate results by using just several elements. The influence of the material inhomogeneity in the geometrically nonlinear behavior of the FGM beam and frame structures is examined and highlighted.

• Structural Engineering and Mechanics
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• v.87 no.1
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• pp.29-46
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• 2023

Critical thermal buckling of functionally graded porous (FGP) sandwich plates under various types of thermal loading is considered. It is assumed that the mechanical and thermal nonhomogeneous properties of FGP sandwich plate vary smoothly by distribution of power law across the thickness of sandwich plate. In this paper, porosity defects are modeled as stiffness reduction criteria and included in the rule of mixture. The thermal environments are considered as uniform, linear and nonlinear temperature rises. The critical buckling temperature response of FGM sandwich plates has been analyzed under various boundary conditions. By comparing several numerical examples with the reference solutions, the results indicate that the present analysis has good accuracy and rapid convergence. Further, the effects of various parameters like distribution shape of porosity, sandwich combinations, aspect ratio, thickness ratio, boundary conditions on critical buckling temperature of FGP sandwich plate have been studied in this paper.

• Steel and Composite Structures
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• v.51 no.4
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• pp.377-389
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• 2024

In the present study, thermoelsatoplastic stresses and displacement for rotating hollow disks made of functionally graded materials (FGMs) has been investigated. The linear elastic-fully plastic condition is considered. The material properties except Poisson's ratio are assumed to vary in the radial direction as a power-law function. The heat conduction equation for the one-dimensional problem in cylindrical coordinates is used to obtain temperature distribution in the disk. The plastic model is based on the Tresca yield criterion and its associated flow rules under the assumption of perfectly plastic material behavior. Exact solutions of field equations for elastic and plastic deformations are obtained. It is shown that the elastoplastic response of the functionally graded (FG) disk is affected notably by the radial variation of material properties. It is also shown that, depending on material properties and disk dimensions, different modes of plastic deformation may occur.

• Steel and Composite Structures
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• v.21 no.1
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• pp.123-136
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• 2016

This work focuses on the behavior of the static analysis of functionally graded plates materials (FGMs) with porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. For this purpose a new refined plate theory is used in this work, it contains only four unknowns, unlike five unknowns for other theories. This new model meets the nullity of the transverse shear stress at the upper and lower surfaces of the plate. The parabolic distribution of transverse shear stresses along the thickness of the plate is taken into account in this analysis; the material properties of the FGM plate vary a power law distribution in terms of volume fraction of the constituents. The rule of mixture is modified to describe and approximate material properties of the FG plates with porosity phases. The validity of this theory is studied by comparing some of the present results with other higher-order theories reported in the literature, the influence of material parameter, the volume fraction of porosity and the thickness ratio on the behavior mechanical P-FGM plate are represented by numerical examples.

• Structural Engineering and Mechanics
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• v.53 no.5
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• pp.981-995
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• 2015

This paper presents a finite element procedure for dynamic analysis of non-uniform Timoshenko beams made of axially Functionally Graded Material (FGM) under multiple moving point loads. The material properties are assumed to vary continuously in the longitudinal direction according to a predefined power law equation. A beam element, taking the effects of shear deformation and cross-sectional variation into account, is formulated by using exact polynomials derived from the governing differential equations of a uniform homogenous Timoshenko beam element. The dynamic responses of the beams are computed by using the implicit Newmark method. The numerical results show that the dynamic characteristics of the beams are greatly influenced by the number of moving point loads. The effects of the distance between the loads, material non-homogeneity, section profiles as well as aspect ratio on the dynamic responses of the beams are also investigated in detail and highlighted.

• Structural Engineering and Mechanics
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• v.57 no.4
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• pp.617-639
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• 2016

In this work, an analytical formulation based on both hyperbolic shear deformation theory and stress function, is presented to study the nonlinear post-buckling response of symmetric functionally graded plates supported by elastic foundations and subjected to in-plane compressive, thermal and thermo-mechanical loads. Elastic properties of material are based on sigmoid power law and varying across the thickness of the plate (S-FGM). In the present formulation, Von Karman nonlinearity and initial geometrical imperfection of plate are also taken into account. By utilizing Galerkin procedure, closed-form expressions of buckling loads and post-buckling equilibrium paths for simply supported plates are obtained. The effects of different parameters such as material and geometrical characteristics, temperature, boundary conditions, foundation stiffness and imperfection on the mechanical and thermal buckling and post-buckling loading capacity of the S-FGM plates are investigated.